Answer
$-\dfrac{1}{2}$
Work Step by Step
Apply Stoke's Theorem $\iint_S curl F\cdot dS=\int_C F \cdot dr$
The equation of the plane with the intercepts can be written as:
$\dfrac{x}{1}+\dfrac{y}{1}+\dfrac{z}{1}=1$
$\implies z=1-x-y$
We know that curl $F=\nabla \times F$
Here, we have curl $F=-yi-zj-xk$
$\iint_S curl F\cdot dS=\iint_D[-y-z-x] dA=-\iint_D dA$
Here, $\iint_D dA$ shows the area of the triangle, which is equal to $=\dfrac{1}{2}(1)(1)=\dfrac{1}{2}$
Therefore,
$\iint_S curl F\cdot dS=\int_C F \cdot dr=-\iint_D dA=-\dfrac{1}{2}$